Mathematical Models for Network Graphs

The article describes the results of the study concerning the effect of the voltage level on current harmonic composition in greenhouses irradiators. It is found that its change affects the level of current harmonics of all types of the studied greenhouse irradiators. With decrease of nominal supply voltage by 10 %, the total harmonic distortion THDi decreases by 9 % for emitters equipped with high pressure sodium lamps (HPSL), by 10 % for emitters with electrode-less lamps and by 3 % for LED based emitters. With increase of nominal supply voltage by 10 %, THDi increases by 23 % for lighting devices equipped with HPSL, by 10 % for irradiators with electrode-less lamps and by 3 % for LED based emitters. Therefore, changes of supply voltage cause the least effect on the level of current harmonics of LED based emitters and then the emitters with electrode-less lamps. Change of the level of supply voltage causes the greatest effect on the level of current harmonics of HPSL based irradiators. Mathematical models of dependence of THDi on the level of supply voltage for greenhouse emitters equipped with LED, electrode-less lamps and HPSL lamps were formulated. These mathematical models may be used for calculations of total current when selecting transformers and supply cable lines for greenhouse lighting devices, for design of new or reconstruction of existing irradiation systems of greenhouse facilities, and for calculation of power losses in power supply networks of greenhouse facilities during feasibility studies for energy saving and energy efficiency increasing projects.

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Mixotrophy in Protists: From Model Systems to Mathematical Models. 2nd Edition

10.3389/978-2-88963-148-3 ◽

2019 ◽

Keyword(s):

Mathematical Models ◽

Model Systems

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Predictive tool for frictional performance of piston ring-pack/liner conjunction

JOURNAL OF MECHANICAL ENGINEERING AND SCIENCES ◽

10.15282/jmes.13.3.2019.19.0445 ◽

2019 ◽

Vol 13 (3) ◽

pp. 5513-5527

Author(s):

J. W. Tee ◽

S. H. Hamdan ◽

W. W. F. Chong

Keyword(s):

Film Thickness ◽

Mathematical Models ◽

Piston Ring ◽

Published Data ◽

Predictive Tool ◽

Frictional Losses ◽

Fundamental Understanding ◽

Minimum Film Thickness ◽

Piston Ring Pack ◽

Ring Pack

Fundamental understanding of piston ring-pack lubrication is essential in reducing engine friction. This is because a substantial portion of engine frictional losses come from piston-ring assembly. Hence, this study investigates the tribological impact of different piston ring profiles towards engine in-cylinder friction. Mathematical models are derived from Reynolds equation by using Reynolds’ boundary conditions to generate the contact pressure distribution along the complete piston ring-pack/liner conjunction. The predicted minimum film thickness is then used to predict the friction generated between the piston ring-pack and the engine cylinder liner. The engine in-cylinder friction is predicted using Greenwood and Williamson’s rough surface contact model. The model considers both the boundary friction and the viscous friction components. These mathematical models are integrated to simulate the total engine in-cylinder friction originating from the studied piston ring-pack for a complete engine cycle. The predicted minimum film thickness and frictional properties from the current models are shown to correlate reasonably with the published data. Hence, the proposed mathematical approach prepares a simplistic platform in predicting frictional losses of piston ring-pack/liner conjunction, allowing for an improved fundamental understanding of the parasitic losses in an internal combustion engine.

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